F.O. Pătrulescu, T. Groşan and I. Pop
The purpose of this paper is to investigate the steady mixed convection boundary layer flow from a vertical frustum of a cone in water-based nanofluids. The problem is formulated…
Abstract
Purpose
The purpose of this paper is to investigate the steady mixed convection boundary layer flow from a vertical frustum of a cone in water-based nanofluids. The problem is formulated to incorporate three kinds of nanoparticles: copper, alumina and titanium oxide. The working fluid is chosen as water with the Prandtl number of 6.2. The mathematical model used for the nanofluid incorporates the particle volume fraction parameter, the effective viscosity and the effective thermal diffusivity. The entire regime of the mixed convection includes the mixed convection parameter, which is positive for the assisting flow (heated surface of the frustum cone) and negative for the opposing flow (cooled surface of the frustum cone), respectively.
Design/methodology/approach
The transformed non-linear partial differential equations are solved numerically for some values of the governing parameters. The derivatives with respect to? were discretized using the first order upwind finite differences and the resulting ordinary differential equations with respect to? were solved using bvp4c routine from Matlab. The absolute error tolerance in bvp4c was 1e-9.
Findings
The features of the flow and heat transfer characteristics for different values of the governing parameters are analysed and discussed. The effects of the particle volume fraction parameter \phi, the mixed convection parameter \lambda and the dimensionless coordinate? on the flow and heat transfer characteristics are determined only for the Cu nanoparticles. It is found that dual solutions exist for the case of opposing flows. The range of the mixed convection parameter for which the solution exists increases in the presence of the nanofluids.
Originality/value
The paper models the mixed convection from a vertical truncated cone using the boundary layer approximation. Multiple (dual) solutions for the flow reversals are obtained and the range of existence of the solutions was found. Particular cases for ?=0 (full cone), ? >>1 and (free convection limit) \lambda>>1were studied. To the authors best knowledge this problem has not been studied before and the results are new and original.
Details
Keywords
Teodor Grosan, Flavius-Olimpiu Patrulescu and Ioan Pop
The purpose of this work is the study of the steady free convection in a square differentially heated cavity filled by a Brinkman bidisperse porous medium. An appropriate…
Abstract
Purpose
The purpose of this work is the study of the steady free convection in a square differentially heated cavity filled by a Brinkman bidisperse porous medium. An appropriate mathematical model considering the Brinkman, momentum and energy interphase terms is proposed. The dependence of the stream functions, isotherms and of the Nusselt numbers on the governing parameters is analysed.
Design/methodology/approach
The both phases of flow and heat transfer are solved numerically using a modified finite difference technique. The algebraic system obtained after discretization is solved using the SOR method. The results are found to be in a significant agreement with the ones presented by the literature for a Darcy bidisperse porous medium and a Brinkman monodisperse porous medium.
Findings
The effects of the governing parameters on stream functions, isotherms and Nusselt numbers are discussed. It has been found that in the case of the Brinkman bidisperse model, the Nusselt numbers decrease compared to the Darcy model, and this behaviour is significant in comparison to the Brinkman monodisperse case.
Originality/value
A mathematical model for the free convection inside a cavity filled by a non-Darcy bidisperse porous medium, based on the Brinkman equation, is used. The effect of Darcy number, Rayleigh number, modified inter-phase heat transfer parameter, modified thermal conductivity ratio and the inertial parameters is studied. To the best of the authors’ knowledge, this problem has not been studied before, and the results are new and original.
Details
Keywords
Iskandar Waini, Anuar Ishak and Ioan Pop
The purpose of this paper is to examine the axisymmetric flow and heat transfer of a hybrid nanofluid over a permeable biaxial stretching/shrinking sheet.
Abstract
Purpose
The purpose of this paper is to examine the axisymmetric flow and heat transfer of a hybrid nanofluid over a permeable biaxial stretching/shrinking sheet.
Design/methodology/approach
In this study, 0.1 solid volume fraction of alumina (Al2O3) is fixed, then consequently, various solid volume fractions of copper (Cu) are added into the mixture with water as the base fluid to form Cu-Al2O3/water hybrid nanofluid. The hybrid nanofluid equations are converted to the similarity equations by using the similarity transformation. The bvp4c solver, which is available in the Matlab software is used for solving the similarity equations numerically. The numerical results for selected values of the parameters are presented in tabular and graphical forms, and are discussed in detail.
Findings
It is found that dual solutions exist up to a certain value of the stretching/shrinking and suction parameters. The critical value λc < 0 for the existence of the dual solutions decreases as nanoparticle volume fractions for copper increase. The temporal stability analysis is performed to analyze the stability of the dual solutions, and it is revealed that only one of them is stable and physically reliable.
Originality/value
The present problem is new, original with many important results for practical problems in the modern industry.
Details
Keywords
Cornelia Revnic, Eiyad Abu-Nada, Teodor Grosan and Ioan Pop
This paper aims to develop a numerical study of the steady natural convection in a rectangular cavity filled with the CuO–water-based nanofluid. It is assumed that the viscosity…
Abstract
Purpose
This paper aims to develop a numerical study of the steady natural convection in a rectangular cavity filled with the CuO–water-based nanofluid. It is assumed that the viscosity of nanofluids depends on the temperature and on the nanofluids volume fraction.
Design/methodology/approach
The mathematical nanofluid model has been formulated on the basis of the model proposed by Buongiorno (2006). The system of partial differential equations is written in terms of a dimensionless stream function, vorticity, temperature and the volume fraction of the nanoparticles, and is solved numerically using the finite difference method for different values of the governing parameters.
Findings
It is found that both fluid flow and heat transfer coefficient are affected by the considered parameters. Thus, the Nusselt number is slowly increasing with increasing volume fraction from 2 per cent to 5 per cent and it is more pronounced increasing with increasing Rayleigh number from 103 to 105.
Originality/value
Buongiorno’s (2006) nanofluid model has been applied for the flow with the characteristics as mentioned in the paper. A comprehensive survey on the behavior of flow and heat transfer characteristics has been presented. All plots presented in the paper are new and are not reported in any other study.
Details
Keywords
M M Rahman, Teodor Grosan and Ioan Pop
The laminar two-dimensional stagnation-point flow and heat transfer of a viscous incompressible nanofluid obliquely impinging on a shrinking surface is formulated as a similarity…
Abstract
Purpose
The laminar two-dimensional stagnation-point flow and heat transfer of a viscous incompressible nanofluid obliquely impinging on a shrinking surface is formulated as a similarity solution of the Navier-Stokes, energy and concentration equations. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The effect of the dimensionless strain rate, shrinking parameter, Brownian motion parameter and thermophoresis parameter on the flow, temperature and nanoparticle volume fraction is investigated in details. The paper aims to discuss these issues.
Design/methodology/approach
The transformed system of ordinary differential equations was solved using the function bvp4c from Matlab. The relative tolerance was set to 10−10.
Findings
It is found that dimensionless strain rate and shrinking parameter causes a shift in the position of the point of zero skin friction along the stretching sheet. Obliquity of the flow toward the surface increases as the strain rate intensifies. The results indicate that dual solutions exist for the opposing flow case.
Research limitations/implications
The problem is formulated for an incompressible nanofluid with no chemical reactions, dilute mixture, negligible viscous dissipation and negligible radiative heat transfer assuming nanoparticles and base fluid are locally in thermal equilibrium. Beyond the critical point λ c to obtain further solutions, the full basic partial differential equations have to be solved.
Originality/value
The present results are original and new for the oblique stagnation-point flow of a nanofluid past a shrinking sheet. Therefore, this study would be important for the researchers working in the relatively new area of nanofluids in order to become familiar with the flow behavior and properties of such nanofluids.
Details
Keywords
Mikhail Sheremet, Teodor Grosan and Ioan Pop
This paper aims to study the magnetohydrodynamic (MHD)-free convection flow in an inclined square cavity filled with both nanofluids and gyrotactic microorganism.
Abstract
Purpose
This paper aims to study the magnetohydrodynamic (MHD)-free convection flow in an inclined square cavity filled with both nanofluids and gyrotactic microorganism.
Design/methodology/approach
The benefits of adding motile microorganisms to the suspension include enhanced mass transfer, microscale mixing and anticipated improved stability of the nanofluid. The model includes equations expressing conservation of total mass, momentum, thermal energy, nanoparticles, microorganisms and oxygen. Physical mechanisms responsible for the slip velocity between the nanoparticles and the base fluid, such as Brownian motion and thermophoresis, are accounted for in the model.
Findings
It has been found that the Hartmann number suppresses the heat and mass transfer, while the cavity and magnetic field inclination angles characterize a non-monotonic behavior of the all considered parameters. A rise of the Hartmann number leads to a reduction of the influence rate of the magnetic field inclination angle.
Originality/value
The present results are original and new for the study of MHD-free convection flow in an inclined square cavity filled with both nanofluids and gyrotactic microorganisms.
Details
Keywords
Mikhail A. Sheremet, Teodor Grosan and Ioan Pop
The purpose of this paper is to study numerically the steady thermal convection in a chamber filled with a nanoliquid affected by a chemical reaction using the single-phase…
Abstract
Purpose
The purpose of this paper is to study numerically the steady thermal convection in a chamber filled with a nanoliquid affected by a chemical reaction using the single-phase nanofluid approximation.
Design/methodology/approach
Water was considered as a host fluid while nanoparticles are aluminum oxide. Homogeneous reactions are analyzed. The nonlinear partial differential equations describing the considered problem are simulated using the finite difference technique.
Findings
The results of streamlines, isotherms, isoconcentrations, nanofluid flow rate, mean Nusselt and Sherwood numbers are discussed. The data demonstrate that the mean Sherwood number increases with the homogeneous reaction rate. Further, nanofluid flow rate can be increased with nanoparticles concentration for high Rayleigh numbers owing to the homogeneous chemical reaction inside the cavity.
Originality/value
Searching the existent references illustrates that the homogeneous-heterogeneous reactions influence on the nanoliquid motion and energy transport within enclosures has not been investigated before. The results of this paper are completely original and the numerical results of the present paper were never published by any researcher.
Details
Keywords
Alin V. Roşca, Natalia C. Roşca, Ioan Pop and Mikhail A. Sheremet
This paper aims to study numerically the steady natural convective heat transfer of a hybrid nanosuspension (Ag-MgO/H2O) within a partially heated/cooled trapezoidal region with…
Abstract
Purpose
This paper aims to study numerically the steady natural convective heat transfer of a hybrid nanosuspension (Ag-MgO/H2O) within a partially heated/cooled trapezoidal region with linear temperature profiles at inclined walls under an effect of uniform Lorentz force. This investigation is useful for researchers studying in the area of cavity flows to know features of the flow structures and nature of hybrid nanofluid characteristics. In addition, a detailed entropy generation analysis has been performed to highlight possible regimes with minimal entropy generation rates.
Design/methodology/approach
The governing equations formulated using the Oberbeck–Boussinesq approach and single-phase nanoliquid model are transformed to a non-dimensional form by using non-dimensional variables. The obtained equations with appropriate boundary conditions are resolved by the finite difference technique. The developed code has been validated comprehensively. Analysis has been performed for a wide range of governing parameters, including Rayleigh number (Ra = 105), Prandtl number (Pr = 6.82), Hartmann number (Ha = 0–100), magnetic field inclination angle (φ = 0–?/2) and nanoparticles volume fraction (φhnf = 0 and 2%).
Findings
It has been shown that inclined magnetic field can be used to manage the energy transport performance. An inclusion of nanoparticles without Lorentz force influence allows forming more stable convective regime with descending heat plume in the central zone, while such a regime was performed for clear fluid only for moderate and high Hartmann numbers. Moreover, the average overall entropy generation can be decreased with a growth of the Hartmann number, while an addition of hybrid nanoparticles allows reducing this parameter for Ha = 30 and 50. The average Nusselt number can be increased with a growth of the nanoparticles concentration for low values of the magnetic field intensity.
Originality/value
Governing equations written using the conservation laws and dimensionless non-primitive variables have been resolved by the finite difference approach. The created numerical code has been verified by applying the grid independence test and computational outcomes of other researchers. The comprehensive analysis for various key parameters has been performed.
Details
Keywords
Mikhail Sheremet, Teodor Grosan and Ioan Pop
The purpose of this paper is to study steady natural convection flow and heat transfer in a triangular cavity filled with a micropolar fluid.
Abstract
Purpose
The purpose of this paper is to study steady natural convection flow and heat transfer in a triangular cavity filled with a micropolar fluid.
Design/methodology/approach
It is assumed that the left inclined wall is heated, whereas the other walls are cooled and maintained at constant temperatures. All four walls of the cavity are assumed to be rigid and impermeable. The micropolar fluid is considered to satisfy the Boussinesq approximation. The governing equations and boundary conditions are solved using the finite difference method of the second order accuracy over a wide range of the Rayleigh number, Prandtl number, vortex viscosity parameter and two values of micro-gyration parameter, namely, strong concentration (n = 0) and week concentration (n = 0.5).
Findings
The results are presented in the form of streamlines, isotherms, vorticity contours and variations of average Nusselt number and fluid flow rate depending on the Rayleigh number, Prandtl number, vortex viscosity parameter and micro-gyration parameter. The flow field and temperature distribution in the cavity are affected by these parameters. The heat transfer rate into the cavity is decreasing upon the raise of the vortex viscosity parameter.
Originality/value
This work studies the effects of vortex viscosity parameter and micro-gyration parameter in a triangular cavity filled with a micropolar fluid on the fluid flow and heat transfer. This study might be useful to flows of biological fluids in thin vessels, polymeric suspensions, liquid crystals, slurries, colloidal suspensions, exotic lubricants; for the design of solar collectors, room ventilation systems and electronic cooling systems; and so on.
Details
Keywords
Natalia C. Roşca, Alin V. Roşca, Teodor Groşan and Ioan Pop
The purpose of this paper is to numerically solve the problem of steady mixed convection boundary layer flow past a vertical flat plate embedded in a fluid-saturated porous medium…
Abstract
Purpose
The purpose of this paper is to numerically solve the problem of steady mixed convection boundary layer flow past a vertical flat plate embedded in a fluid-saturated porous medium filled by a nanofluid. The non-Darcy equation model along with the mathematical nanofluid model proposed by Tiwari and Das (2007) has been used.
Design/methodology/approach
Using appropriate similarity transformations, the basic partial differential equations are transformed into ordinary differential equations. These equations have been solved numerically for different values of the nanoparticle volume fraction, the mixed convection and the non-Darcy parameters using the bvp4c function from Matlab. A stability analysis has been also performed.
Findings
Numerical results are obtained for the reduced skin-friction, heat transfer and for the velocity and temperature profiles. The results indicate that dual solutions exist for the opposing flow case (λ<0). The stability analysis indicates that for the opposing flow case, the lower solution branch is unstable, while the upper solution branch is stable. In addition, it is shown that for a regular fluid (φ=0) a very good agreement exists between the present numerical results and those reported in the open literature.
Research limitations/implications
The problem is formulated for three types of nanoparticles, namely, copper (Cu), alumina (Al2O3) and titania (TiO2). However, the paper present results here only for the Cu nanoparticles. The analysis reveals that the boundary layer separates from the plate. Beyond the turning point it is not possible to get the solution based on the boundary-layer approximations. To obtain further solutions, the full basic partial differential equations have to be solved.
Practical implications
Nanofluids have many practical applications, for example, the production of nanostructured materials, engineering of complex fluids, for cleaning oil from surfaces due to their excellent wetting and spreading behavior, etc.
Social implications
Nanofluids could be applied to almost any disease treatment techniques by reengineering the nanoparticle properties.
Originality/value
The present results are original and new for the boundary-layer flow and heat transfer past a vertical flat plate embedded in a porous medium saturated by a nanofluid. Therefore, this study would be important for the researchers working in porous media in order to become familiar with the flow behavior and properties of such nanofluids.